Answer:
see explanation
Step-by-step explanation:
The roots are the points on the x- axis where the graph crosses
The roots are (- 3, 0 ) or (1, 0 )
The turning point is at (- 1, - 4 ) ← where the graph turns
Answer:
$103.6 left
Step-by-step explanation:
First, multiply the amount she earns an hour times how many hours she worked:
9.25 x 14 = 129.5
Then divide the total by 1/5:
129.5 / 5 = 25.9
Then subtract that value from the total:
129.5 - 25.9 = 103.6
$103.6 is your answer
Hope this helps!
<h2>
Hello!</h2>
The answer is:
The ball will hit the ground after ![t=2.47s](https://tex.z-dn.net/?f=t%3D2.47s)
<h2>
Why?</h2>
Since we are given a quadratic function, we can calculate the roots (zeroes) using the quadratic formula. We must take into consideration that we are talking about time, it means that we should only consider positive values.
So,
![\frac{-b+-\sqrt{b^{2} -4ac} }{2a}](https://tex.z-dn.net/?f=%5Cfrac%7B-b%2B-%5Csqrt%7Bb%5E%7B2%7D%20-4ac%7D%20%7D%7B2a%7D)
We are given the function:
![h=-5t^{2}-3t+38](https://tex.z-dn.net/?f=h%3D-5t%5E%7B2%7D-3t%2B38)
Where,
![a=-5\\b=-3\\c=38](https://tex.z-dn.net/?f=a%3D-5%5C%5Cb%3D-3%5C%5Cc%3D38)
Then, substituting it into the quadratic equation, we have:
![\frac{-b+-\sqrt{b^{2} -4ac} }{2a}=\frac{-(-3)+-\sqrt{(-3)^{2} -4*-5*38} }{2*-5}\\\\\frac{-(-3)+-\sqrt{(-3)^{2} -4*-5*38} }{2*-5}=\frac{3+-\sqrt{9+760} }{-10}\\\\\frac{3+-\sqrt{9+760} }{-10}=\frac{3+-\sqrt{769} }{-10}=\frac{3+-27.731}{-10}\\\\t1=\frac{3+27.731}{-10}=-3.073s\\\\t2=\frac{3-27.731}{-10}=2.473s](https://tex.z-dn.net/?f=%5Cfrac%7B-b%2B-%5Csqrt%7Bb%5E%7B2%7D%20-4ac%7D%20%7D%7B2a%7D%3D%5Cfrac%7B-%28-3%29%2B-%5Csqrt%7B%28-3%29%5E%7B2%7D%20-4%2A-5%2A38%7D%20%7D%7B2%2A-5%7D%5C%5C%5C%5C%5Cfrac%7B-%28-3%29%2B-%5Csqrt%7B%28-3%29%5E%7B2%7D%20-4%2A-5%2A38%7D%20%7D%7B2%2A-5%7D%3D%5Cfrac%7B3%2B-%5Csqrt%7B9%2B760%7D%20%7D%7B-10%7D%5C%5C%5C%5C%5Cfrac%7B3%2B-%5Csqrt%7B9%2B760%7D%20%7D%7B-10%7D%3D%5Cfrac%7B3%2B-%5Csqrt%7B769%7D%20%7D%7B-10%7D%3D%5Cfrac%7B3%2B-27.731%7D%7B-10%7D%5C%5C%5C%5Ct1%3D%5Cfrac%7B3%2B27.731%7D%7B-10%7D%3D-3.073s%5C%5C%5C%5Ct2%3D%5Cfrac%7B3-27.731%7D%7B-10%7D%3D2.473s)
Since negative time does not exists, the ball will hit the ground after:
![t=2.473s=2.47s](https://tex.z-dn.net/?f=t%3D2.473s%3D2.47s)
Have a nice day!